1. Field of the Invention
The invention generally relates to data communication channels with a varying peak-to-average power ratio, and in particular, to radio frequency (RF) or wireless transmissions in which peak-to-average ratio makes linearity challenging.
2. Description of the Related Art
In a data communication system, there are typically 3 sources of imperfection: (1) Band-limited channel; (2) Noise; and (3) Distortion. The first, “band-limited channel,” is typically the result of parasitic impedances that reduce the bandwidth of the channel. Linear equalizers and the like are usually used to correct this imperfection. The second, “noise,” is the result of random processes in the circuit and channel. This imperfection is typically tolerated rather than corrected. The third, “distortion,” is the result of amplifier/block nonlinearity. Typical non-linearities in a data communication signal processing system are caused by analog circuit blocks.
In a radio or RF front end, the following analog circuit blocks contribute to the overall nonlinearity of the system: (i) Low noise amplifier (LNA); (ii) Down Converter; (iii) variable gain amplifier (VGA); (iv) Filter; (v) Up Converter; (vi) Pre-Power Amplifier; (vii) Power Amplifier; and the like.
Typically, a nonlinearity is of a “compressing” nature, in which the small signal gain of the amplifier decreases as the input signal becomes larger. Nonlinearities in a TX-RX link of a data communications system can degrade the bit error rate (BER) performance of the system by, for example, introducing the following: (i) Harmonics (frequency components that are integer multiples of the input frequencies); (ii) Gain Compression (the decrease in small signal gain as the input signal becomes larger); (iii) Desensitization or blocking (weak signals experience a increasingly smaller gain in the presence of larger signals); (iv) Cross Modulation (an artifact whereby the modulation of an interferer is transferred to a weaker desired signal); and (v) Intermodulation (frequency components that are sums and differences of integer multiples of two or more sinusoidal inputs).
Many texts have been written on the effects of nonlinearity in RF systems, such as RF Microelectronics by Behzad Razavi. (See Section 2.1.1 in the first edition). A memory-less nonlinear system can be represented with the input-output relationship as shown in Equation 1.y(t)=N[x(t)]=a1x(t)+a2x2(t)+a3x3(t)+  (Eq. 1)
The functional N in Equation 1 represents the overall nonlinearity of the channel. The goal of most linearization techniques is to estimate the inverse function N−1 that can be applied somewhere in the system to reduce the effects of the nonlinearity.
Most systems are both nonlinear and dynamic (the output depends on past values of the input). This fact can complicate the issue of linearization, but for the purposes of the analysis herein, dynamic affects are ignored. It will be shown that substantial improvements are still achieved with this simplification.
Many linearization techniques pre-distort the signal before an analog circuit introduces a nonlinearity such that the net effect is a relatively linear system. This concept is illustrated in Equation 2.y(t)=N[PRE[x(t)]]≈x(t);PRE[·]≈N−1[·]  (Eq. 2)
It should be noted that a function that returns x(t) is typically not sought; but rather, βx(t), i.e., a scaled version of x(t), is sought. For simplicity, however, the scaling will be ignored. Embodiments of the invention use post-compensation in the manner shown by Equation 3.y(t)=POST[N[x(t)]]≈x(t);POST[·]≈N−1[·]  (Eq. 3)Estimating the Inverse Nonlinearity Functional, N−1[.]
One of the difficulties with any linearization technique is estimating N−1[.], whether in the form PRE[.], or POST[.], because the original distorting nonlinearity, N[.], is unknown and changes with process, voltage, and temperature (known as “PVT”), and age. This task is further complicated by the earlier-mentioned problem of a system being both non-linear and dynamic.
A feedback system of some sort is usually established to determine N′−1[.]. A feedback system uses the computation of an error between the desired response and the actual response. This error can be explicit or implicit, and deterministic or noisy.
With explicit error, the error is calculated directly as the difference between the actual signal and the known desired signal. With implicit error, the desired signal may not be known directly but is inferred indirectly through some kind of indicator or the like.
It can also be the case that while the error can be computed, the computation produces error signal and noise (as will be shown below). It is sometimes more efficient to calculate an error if the included noise can be tolerated. The reader is referred to the classic text Automatic Control Systems, by Benjamin C. Kuo for details on feedback systems.
Current state of the art for linearization techniques can be broken into two categories: pre-distortion, and post-compensation. Examples of Pre-Distortion techniques can be found, for example, in the following: (i) U.S. Pat. No. 6,798,843 to Wright, et al.; (ii) U.S. Pat. No. 6,940,916 to Warner et al.; (iii) U.S. Pat. No. 6,973,138 to Wright, et al.; (iv) U.S. Pat. No. 4,811,097 to Ritter and Zortea; (v) International Publication WO03081870 by Huang Xinping, titled Adaptive Predistorter Based on the Probability Distribution Function of the Output Amplitude.
Examples of Post-Compensation techniques can be found, for example, in the following: U.S. Pat. No. 7,002,410 by Jeong, et al.; and Nonlinear distortion correction in comms channel paths by Batruni of Optichron, Planet Analog, 29, March 2006.